Does anybody know something similar to Google Maps for using in a Java Desktop Application? The only functionality I'm interested in is marking a point on the map and find the coordinates of that spot.

A popular alternative is OpenStreetMap. Unfortunately, I can't provide exact implementation details, as I haven't tried it yet, but it certainly seems to be possible to use it in Java, according to their Wiki.

To embed them in a Java app you can easily embed a webpage with JavaFX 2 webview (javafx 2 components can be used in swing too). Or use a library they provide (if any) or implement the api and rendering yourself.